The cetacean was found dead in Goolwa, just over 60 kilometers south of Adelaide, the state's Department of Primary Industries and Regions said.
"While the detection in the common dolphin is a new development in Australia, there is evidence of dolphins and porpoises catching H5 bird flu overseas," the department said.
"Dolphins would not commonly eat birds but it is not unusual for them to sometimes interact."
Australia was for years the only continental landmass free of the H5 strain, which has caused severe disease and death in poultry and wild birds worldwide.
There have been no cases detected in poultry or in the country's agriculture production.
